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3 years ago

The length of one leg of a right triangle is 8 centimeters shorter than the

1 answer:

3 0

${34}^{2} + {b}^{2} = {42}^{2} \\ 1156 + {b}^{2} = 1764 \\ 1156 - 1156 + {b}^{2} = 1764 - 1156 \\ {b}^{2} = 608 \\ \sqrt{ {b}^{2} } = \sqrt{608} \\ b = 24.7$
I used the Pythagorean formula, which is a² + b² = c².
a² and b² are the two side legs while c² is the hypotenuse.
One of the side is 42 - 8 = 34 cm.

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Which point is not on the graph of the equation y=10+x

RSB [31]

Answer:

C. (8, 2)

Step-by-step explanation:

To find which point is not on the graph, find which set of coordinates makes the equation incorrect.

When plugged into the equation, the point (8, 2) makes it incorrect:

y = 10 + x

2 = 10 + 8

2 = 18

2 $\neq$ 18

The equation is incorrect because 2 is not equal to 18.

So, the point that is not on the graph is C. (8, 2)

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2 years ago

Write a equation of a hyperbola given the foci and the asymptotes

professor190 [17]

Solution:

The standard equation of a hyperbola is expressed as

$\begin{gathered} \frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1\text{ \lparen parallel to the x-axis\rparen} \\ \frac{(y-k)^2}{a^2}-\frac{(x-h)^2}{b^2}=1\text{ \lparen parallel to the y-axis\rparen} \end{gathered}$

Given that the hyperbola has its foci at (0,-15) and (0, 15), this implies that the hyperbola is parallel to the y-axis.

Thus, the equation will be expressed in the form:

$\frac{(y-k)^2}{a^2}-\frac{(x-h)^2}{b^2}=1\text{ ----equation 1}$

The asymptote of n hyperbola is expressed as

$y=\pm\frac{a}{b}(x-h)+k$

Given that the asymptotes are

$y=\frac{3}{4}x\text{ and y=-}\frac{3}{4}x$

This implies that

$a=3,\text{ and b=4}$

To evaluate the value of h and k,

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1 year ago

Find the inverse of f(x)= -x + 3

inna [77]

Let g the inverse function of f.

The most important property of g and f being inverses of each other, is that

g(f(x))=x, also f(g(x))=x

so, what one function 'does' to x, the other 'undoes' it.

Thus, we have:

f(g(x))=x and alos f(g(x))= -g(x)+3, from the rule

thus :

-g(x)+3=x

-g(x)=x-3

g(x)=-x+3

check: f(g(x))=f(-x+3)=-(-x+3)+3=x-3+3=x

Answer: the inverse of f is g, such that g(x)=-x+3

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3 years ago

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alexandr402 [8]

$8.5, $\frac{68}{8} = 8.5$

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3 years ago

Which statement below about roots is false.Immersive Reader (5 Points) Simplified radicals have a positive and a negative root.

scoray [572]

Answer:

Statement (B)

Step-by-step explanation:

Which statement below about roots is false?

Let's arrange the statements by assigning option-letters a, b, c, d to them.

(A) Simplified radicals have a positive and a negative root.

This is true, as the root of any number is either a positive or a negative; especially if the rooting index is an even number like 2 or 4. For example, the square root (when the index is 2) of 9 is either +3 or -3. To check, find their squares. +3 x +3 = 9 and -3 x -3 = 9.

(B) A radicand is the symbol used when working with roots.

This statement is false, as the name for the symbol used in root operations is "radical symbol". A radicand is the number or expression whose roots are about to be found. It is the expression that lies under or inside the radical symbol!

Exponents are the powers to which mathematical expressions are raised. Roots are the indexes by which mathematical expressions are divided. Exponents are hence the opposites or inverses of roots.

(D) Roots can be squared, cubed, quadrupled, or raised to higher powers.

Yes! The root of a mathematical expression or figure can be raised to any number or power, be it 2 (square), 3 (cube), 4 (quadruple), 5 (quintuple) or 100 (cent).

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3 years ago